I was compelled to put this timeline together after someone told me that they were under the impression that a specific beat 'em up was more seminal than it actually is. So instead of offering a lengthy explanation I put together the chronological facts. As it stands, it's the cursory data that is easily available on Wikipedia (all of the timeline's articles link to the corresponding Wikipedia entry) but I may supplement it with more interesting information about mechanical evolution if enough people show interest.
A little bit of information on the "ages" in the timeline; the different ages are, for me, about design and aesthetic sensibilities, and not about mechanical properties, although these tend to dramatically change between the ages.
The First Age
The First Age obviously encompasses the birth and early childhood of beat 'em ups. Contrary to what many people believe, I don't feel like Kung Fu Master was the first beat 'em up, which is why the first age starts with Renegade in 1986. The rest of the age is comprised of traditional beat 'em ups that took place in side scrolling levels. This age is noted for its simple gameplay and simple graphics; technology constraints enforced the simplicity.
The Second Age
The Second Age began with Aliens Vs Predator, which brought a marked increased in mechanical sophistication and nuance. Every aspect of the beat 'em up experience was improved by a substantial margin. Most of this select handful of high quality games were created by Capcom on their CPS2 hardware. This brief period was the golden apex of the arcade beat 'em up. While 2nd age beat 'em ups would continue to periodically emerge, I consider Capcom's 1997 Battle Circuit the formal end of the age.
The Dark Age
Unfortunately, the very promising Second Age was decapitated by the advent of 3d gameplay on the home console. This brief Dark Age is comprised of a few remarkably poor titles that were produced and marketed on the excitement of early 3d gameplay. These games are cumbersome, stiff, and underdeveloped as combat experiences. Before you yell at me and tell me how much you loved one of these games and that I'm a dumb jerk, just know that I'm not negating their nostalgic value. As beat 'em ups, they were definitely the awkward teenage years of the genre.
The Third Age
The Third Age was ushered in by Devil May Cry 1 and put the beat 'em up back in the spotlight with 3d gameplay that finally looked and felt good. While I'm not necessarily implying that the games in this age are all great (I personally find DMC1 very stiff and unenjoyable at this point and plenty of these games are just ok), they are built on more mature design principles. The third age has been a 10+ year renaissance, only losing momentum in recent years. There are games in all ages I have left out, but I intentionally left a lot of them out because I don't believe they contributed to the timeline. But by all means, let me know if you'd like a game inserted by telling me why you feel it belongs. And besides, I might have just forgotten it. ;)